£ 



METHOD 

of finding the true cause of the 
Acceleration and Retardment of the 

Eclipses of Jupiter's Satellites 

without making use of 
the Progressive Velocity of Light, 
or the Movement of Light, 



-BY- 






Capt. JAMES W. NORCROSS, 

716 Chambkr of Commerce Building, India St., Boston. 



Entered by Act of Congress the 15th of June, 1893. 
By James Winchell Norcr/jss. 

boston, mass. /^ 

^Jfi 10 1893* 




PREFACE. 



Like the prospector, who after long audi weary searching, has picked 
up an object with the shimmer of gold on its surface, feeling sure he 
had in his grasp the precious metal itself, only to find he held but dross, 
so has it been with the writer. Many trials, disappointments and some 
bitter lessons have engendered a certain timidity that has delayed the 
publication of this work, fearing that by some misconception or over- 
sight he may have been misled. But careful examination reveals no 
flaw. All appears to be in perfect harmony with natural laws and teach- 
ings of the illustrious founders of modern astronomy. Not a glimpse 
of anything that could add to or change what he now ventures to put 
forth having appeared, and trusting his judgment has not erred, grate- 
ful if he has been permitted to be the instrument for unearthing truth 
from the error where it has so long lain buried, he now submits this 
problem to the attention and consideration of authorities so greatly 
superior to himself, trusting his efforts may have aided to promote the 

advancement of astronomy. 

The Author. 






Yll^ 



EXPLANATION. 



After a long and patient search the writer is now fully convinced 
that he has found the true cause of the variation and that the Roerner 
theory of transmission has nothing at all to do with it.^-He has never 
doubted a regulated speed of light in the atmosphere, but has always 
questioned the right to make use of an ether made to pervade all space 
and invented to be used as the means of regulating its movement. 
What is the ether ? Certainly something hard to conceive. A some- 
thing not subject to the law of gravitation, nor capable of resistance, 
and yet it is called on to perform the same service as the atmosphere 
and by means of vibrations convey light at a regular speed of 192,000 
miles a second, and to cause it to move at the same speed in the densest of 
our atmosphere. This being so directly contrary to well-known natural 
laws has been the steady cause for stubborn disbelief in the whole theory, 
and two brief remarks that will be obvious will show the reason why : 
First — In nature's phenomena, such as heat, electricity, sound, and in 
which we may safely include light, the speed varies with variation in 
density. In this case these conditions are particularly applicable to light 
which by the Roemer theory passes from the impalpable ether, all through 
the different strata of the atmosphere to the lowest or densest, where the 
speed is estimated. Second — None of these phenomena can have a 
continued regular speed in any resisting medium. However quickly 
they might enter, their speed would naturallv be retarded until their 



4 

power of penetration was exhausted. This, however, will not affect 
-rration as the J ew extra miles consequent to low altitudes would have 
but an insensible effect. In consequence of the above the writer is a 
firm believer in the theory of a perfect vacuum in space that existed 
previous to the invention of the theory of ether, and that light pas 
instantaneously, only being retarded when it plunges into a resisting 
medium, such, for example, as the atmosphere- The fact remains 
: since Dr. Bradley applied the motion of light to aberration the 
theory has been accepted by all great authorities, is the only one in use. 
and gives approximate, but never accurate results. Rut its application 
by Dr. Bradley was the relative speed of light and the earth's proper 
motion, the very thing that has finally led up to the solution which is 
to follow. As applied to the eclipses, it is only an artificial division of 
space and has never weakened the writer in his belief that the real cause 
of the phenomena lay somewhere else, but where? With absolutely no 
data to go by. it was hunting a needle in a haystack. Gleaning in all 
the fields of astronomical teaching produced but straws to be after 
thrown aside as useless, but with an innate certainty that the needle 
was in the stack, it was always a case of try again. Without further 
enumeration of trials and disappointments the thought occurred that 
when about to be eclipsed the satellites have a temporary proper motion 
of their own. independent of the motion as carried along by Jupiter 
and nearly on the same radius as the planet itself, and as the proper 
motion of the earth relative to the motion of light affects the longitude 
of the heavenly bodies, why should not the relative motion of the earth 
and satellites affect their longitude ? The first trial was in applying 
aberration to the method as seen further on. and the result with two 
z: options was very satisfactory and led right up to the truth. The 
method by aberration is inserted, for there are great possibilities in this 
Little l. )" measure that practical astronomers will see and know well how 
to make use of. 

This question finally resolves itself into the relative proper motion of 
the earth and satellites combined with distance. Light or movement 
of lisht having; nothing at all to do with it. 



Method, making use of Aberration, max. 20". 

Calling mean distance (Radius Vector) of Jupiter, 494,000,000 m. 

i% Jupiter's proper motion, . . ... 8 m. 

Earth's proper motion, .... 19 m. 

Wk Periodic time of first satellite, . 42h., 27m. 33s. 

The Radius Vector of first satellite, 225,000 m. 

Gives proper motion 9.318 + Jupiter 8 =17, 318 m. 

" Aberration, . . . . . ■ 18". 23. 

Calling mean distance in opposition 4J times the 
radius of Earth's orbit ^ T and in conjunction 
6J times -^. 
Gives Angular effect in Opposition, . . 4". 290. 

kt " Conjunction, . . 2".918. 

u Constant mean aberration in Opposition, — 15 ".7 10. 
" ' 4 k4 4W •' Conjunction, + 22".918. 



" Difference, affects long, of satellite, 7". 208. 

Jupiter's mean motion, . . . I"in292s. 

Satellites at immersion, . . . 1" in 134s. 

Difference from Con. to Opp. 7".208 X 134s = 16m. 4s. 

Calling Periodic time fourth satellite, . . 16d. 16h. 31m. 50s. 

" Radius Vector, .... 999,000 m. 

Gives Proper motion at immersion 4.354 -\- 8 12,354 m. 

Aberration, ..... 13". 

Angular effect in Opposition, . . 3 ".05. 

" fct 4t k * Conjunction, . . 2 ".08. 

Constant mean aberration in Opposition, — 16". 95. 
kt •' kt ' k '• Conjunction-(-22" 08. 

Difference, affects long, of satellite, 5". 13, 

" Motion, 1" in 189s. X 5".13 . . = 16m., 8s. 

Deduct for 1,000,000' greater distance first sat. 3s. = 16m., 5s. 

Difference, ...... Is. 

When, as seen farther on, we add 60s. for change of distance the 
accumulated time carrying it to 17m., which is too great. 



6 

This being the mean, and as the result of this method is relative 
speed combined with distance, of course, on account of Jupiter's eccen- 
tricity, 2T the accumulated time will be greater where the distance is 
less than the mean, so that the + 60s. and — 44s. will cause the accu- 
mulated time stand 16m., 04s. 4- 60s. = 17m., 04s. 
16m., 04s. — 45s. = . . . 15m., 19s. 
Whole variation in accumulated time. . . . lm., 45s. 
Right here it is seen that aberration and the Roemer theory of transmis- 
sion diverge, for whilst by the former the variation cannot exceed lm. 
45s., by the latter the variation can be as great as 3m. 30s., a difference 
of lm. 45s. It is obvious that the two principles are not the same, 
although aberration was the plank on which the Roemer theory was floated. 
It is also seen that this method makes the accumulated time too great 
and it was easy to see that the reason lay in not being the true propor- 
tion — earth's motion to speed of light and earth's motion to motion of 
the satellites. Aberration is but the offspring of relative motion, and 
as we are looking for the very same thing (a change of longitude, but 
on a much smaller scale), it is the relative motion, a principle that 
produces aberration, we must make use of. Repeating the formula 
with relative speed, combined with distance, we get as follows : 
Calling Jupiter's mean Radius Vector, . 494,000,000 m. 
*' Proper motion in a second, . . 8 m., 
'• Earth's proper motion in a second, 19 m. 
" Periodic time first satellite, . . 42h., 27m., 33s. 
• ; Radius Vector, .... 225,000 m. 
Gives Proper motion at immersion 9.318 -|- b 17.318 m. 
Calling Jupiter's distance, when in Opposition. 4^ 
times the earth, Radius Vector ^ T and when 
in Conjunction 6J times -^-. 
Gives 17.318—^-17 angular effect in Opposition = 4.076 m. 

" 17.318-^-25 ' Conjunction 2.772 m. 

Constant mean aberration in Opposition = 14". 921 — 

" Conjunction = 21". 772 + 
Difference affects longitude of satellite, 6". 848 



Jupiter's mean movement 1" in 292s.=satellite 134s 

X6".848 

Variation of distance on account of eccentricity, 



Whole variation, 



Fourth Satellite. 



= 


15m.. 


1 7s 


, -(-56s. 


, 16m 


13s, 


— 44s 


. 14m 


33s, 


= 


= 1 m . . 


40?, 


16d., 16h., 31m 


., 50s. 




999,000 m. 






12,354 m. 






2.908 






1.976 






16".092 — 






20". 976 + 






4". 844 






15m. 


, 23s. 




-f-56s.. 


16m., 


19s. 


—44s., 


14m., 


39s. 



Calling Periodic time. 

Radius Vector, 
Gives Proper motion at immersion 4.354 — |— 8 
Angular effect in Opposition, . 
kt Conjunction 
Constant mean aberration in Opposition, 
"■ lt •• l * '■ Conjunction, 

• w Difference, longitude of satellite 

Satellite moves 1" in 189s. X 4".884 = 
By variation of distance, 

• 4 . — 44s. ,1 

lm , 40s, 
There being 112 eclipses Con. to Opp. gives mean 8.189s. for each 
eclipse 

By the theory of transmission we find a difference of lm. 45s. in 
excess of this difference, which, divided by 112, gives less than Is. for 
each eclipse.* 

A difference is always found between the observed and calcu- 
lated eclipses and attributed to probable irregularities in the move- 
ment of the satellite in its orbit. It is well to point out that such 
irregularities cannot be. The periodic times are found to be uniform, 
and as an entire revolution must necessarily take plane for each eclipse, 
irregularities, if they exist, would all be covered in. Besides, the dif- 
ferences -|- 60s. and — 45s. makes the true proportion, variation by 
eccentricity is to mean radius as lm. 45s is to mean accumulated time 
15m. 17s. The trouble lies in too great a range of variation in the 

* Of course the 1'45" difference between the Eoemer theory and Relative Speed is an 
accumulation of a half revolution of Jupiter in its orbit which, for successive years, 
would appear but a very small error. 



accumulated time by the theory of transmission of light. By making 
use of the first and fourth satellites it is shown that all will come beau- 
tifully into line in accordance with Kepler's third law. Although in 
these calculations the writer has not aimed at absolute correctness, the 
very small difference of time 3s. r counting greater distance between the 
first and fourth satellites, shows conclusively that they are very near the 
true quantities. Absolute correctness will not be obtained until the 
method is properly tabulated, which he has neither the time nor facili- 
ties to do. When that is done, it will give terrestrial longitude with 
perfect accuracy, what the Roemer theory can never do. With the 
exception of that theory this method changes nothing. But on the 
contrary enhances the value of aberration which by one of the fortuit- 
ous accidents that sometimes occur was derived from the relative mc ~ - 
ment of light and the earth's motion. Summing up we find the whole 
mean effect in longitude, which we may call, so to speak, in aberration 
of aberration to be in time 15m. 1 7s. That this quantity varies -(- 60s. 
ami — t " - . on account of eccentricity and the motion of the earth in 
its orbit. The mean for each eclipse (1st satellite) 17a — 1 1_ = 
8.189s~ or about ^ of 1" iu longitude. It is obvious that if there 
was no change of distances as in the sun. or as apparently so in the 
?*:.:■= : ... - ■ ■ . " . . -. - _ ■: - . : — :' : _ - - :e '.".:: -f —:"".: z :::■:: :: 
There would be no variation in the times of the eclipses and that is all 
there is in it- The true solution of this problem casts no reflection 
on the illustrious Roemer. Had the observations of Dr. Bradley pre- 
ceded his observations of the eclipses of the satellites, who knows but 
what the acute intellect of the former might have conceived the idea 
that light would be retarded on entering the atmosphere, and the prin- 
ciple of relative speed developed, that the latter would have applie 
to the motion of the earth and the satellites. For the time in which he 
lived his thought nevertheless was a brilliant conception, that has per- 

. . _ - '. v. r _ : . ■: . - - : _; . r._ ;• _ ~ :— :.i- '. :z ^:rii: z :■:•'. :_ l : : ~\-Z 

the world aberration, which in its turn has now given the truth. If in 
solving this problem the construction is clumsy and awkward the writer 
."_ ~ _ "- " ~ :.:. — _ - .z-z t._-:..t .: ::: 12 : .-Zr'z-: : zy~.'i:z^ _ :' 
this import. 



